[FOM] The characteristic S5 axiom and the ontological argument

Peter LeFanu Lumsdaine plumsdai at andrew.cmu.edu
Fri Apr 10 10:22:55 EDT 2009

On 9 Apr 2009, at 20:21, Vaughan Pratt wrote:

> From a mathematical standpoint I find it remarkable that those in
> possession of an argument for the existence of something seem to be  
> able
> to get unique existence out of the same argument.

Surely it's from a mathematical standpoint that this should seem least  
surprising?  We have plenty of definitions of things which, if they  
exist, are automatically unique:  a two-sided identity for a binary  
multiplication; a least element in a poset; anything defined by a  
universal property (unique up to isomorphism, in this case)...

If "a god" were a local, physical object, then yes, a robust  
statistical argument for the existence of one would have to suggest  
the existence of many.  But I don't think those who make or enjoy such  
arguments conceive of "a god" as such an object.

> Plantinga has made a
> career of creating God from logic and statistics.  If, as he argues,  
> it
> is likely that an entity exists meeting our criteria for godliness,  
> then
> it would seem even more likely that there are say a hundred of them  
> than
> one, and more likely still a thousand.
> Given the size of the universe, any predicate whose satisfiability is
> within the realm of possibility is highly likely to be satisfied not
> just once but many times.  Any conception of God that happens, for
> whatever combination of reasons, to rule out the possibility of
> membership of God in this universe ensures of course that God does not
> exist in it.  Any other conception however is highly likely to admit
> many instances.  By far the least likely outcome is exactly one God,
> whatever conception of God one uses.  Monotheism is therefore the  
> least
> plausible of all possible religious beliefs.  That more than half the
> planet is monotheistic is yet another bit of evidence for the thesis
> that humans aren't very good at probability.

Peter LeFanu Lumsdaine
Carnegie Mellon University

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